Following my problem with su earlier last week, I figured I'd better get a
refresher on permissions before I really get myself in trouble.

I guess I never knew what the "s" was for in:
-rwsr-xr-x

I checked out `info chmod' and various other places, including a few books
I have and came up empty on what the plain-english meaning of `4000 Set
user ID on execution' means. I checked the archives and only came up with
answers to the same question that consisted solely of "s - Set user ID or
group ID on execution," but NOT what difference this makes.

Can anyone explain this to me in plain english? Like, what the difference
is between chmod 4750 and chmod 750 -- and how it effects the files'
execution?

All I have known is that for binaries I want to restrict access to, I have
always chgrp special_group special_files and chmod 4750 special_files.